Abstract

The probability hypothesis density (PHD) filter is well known for addressing the problem of multiple human tracking for a variable number of targets, and the sequential Monte Carlo (SMC) implementation of the PHD filter, known as the particle PHD filter, can give state estimates with nonlinear and non-Gaussian models. Recently, Mahler et al. have introduced a PHD smoother to gain more accurate estimates for both target states and number. However, as highlighted by Psiaki in the context of a backward-smoothing extended Kalman filter, with a non-linear state evolution model the approximation error in the backward filtering requires careful consideration. Psiaki suggests to minimise the aggregated least-squares error over a batch of data. We instead use the term retrodiction PHD (Retro-PHD) filter to describe the backward filtering algorithm in recognition of the approximation error proposed in the original PHD smoother, and we propose an adaptive recursion step to improve the approximation accuracy. This step combines forward and backward processing through the measurement set and thereby mitigates the problems with the original PHD smoother when the target number changes significantly and the targets appear and disappear randomly. Simulation results show the improved performance of the proposed algorithm and its capability in handling a variable number of targets.